Research Methods

Factor Analysis Resources
Understanding & Using Factor Analysis in Psychology & The Social Sciences

 

Understanding Factor Analysis

What is Factor Analysis?

  • Factor analysis is a correlational technique to determine meaningful clusters of shared variance.
  • Factor Analysis should be driven by a researcher who has a deep and genuine interest in relevant theory in order to get optimal value from choosing the right type of factor analysis and interpreting the factor loadings.
  • Factor analysis beings begins with a large number of variables and then tries to reduce the interrelationships amongst the variables to a few number of clusters or factors.
  • Factor analysis  finds relationships or natural connections where variables are maximally correlated with one another and minimally correlated with other variables, and then groups the variables accordingly.
  • After this process has been done many times a pattern appears of relationships or  factors that capture the essence of all of the data emerges.
  • Summary: Factor analysis refers to a collection of statistical methods for reducing correlational data into a smaller number of dimensions or factors

Factor Analysis Readings

Introductory

Advanced

(More mathematical, graduate-level, &/or non-social science orientation)

More

Types of Factor Analysis

  • Exploratory Factor Analysis
    • Principle Components
    • Principle Axis Factoring
  • Confirmatory Factor Analysis

Frequently Asked Questions

 

What is the difference between PC and PAF?

  • Principle Axis Factoring (PAF) analyzes only the variance in the items that is shared with other items.  That's why the communalities will be less than 1 (they represent the proportion of variance in an item explained by the other items).  PAF is generally considered best for exploring the underlying factors for theoretical purposes For example, PAF is usually driven by questions such as
    • "How many factors?"
    • "What are the factors?"
    • "What is the relationship amongst the factors?"
       
  • Principal Components (PC) analyzes all the variance in the items.  That's why the communalities are all 1 (representing 100% of the variance of each item being included in the analysis).  PC is generally considered the best method for the pragmatic purposes of data reduction.  Data reduction means that the goal is to simplify, by summarising the variance associated with, say, 30 items down to, say, 5 factors.  The goal is to capture the lion's share of the variance in the 30 items using a smaller number of factors.  PC is most common used in the process of
    • mental test development and for
    • developing composite scores for subsequent analyses (e.g., using ANOVA or MLR)

What is a Simple or Clean Factor Structure?

  • A simple or clean factor structure is evident when each item in a factor analysis loads highly on one factor and lowly on other factors.
  • Note that the 'appearance' of a simple factor structure can occur by suppressing loadings below (typically) .1, .2., .3, etc.  Suppression of factor loadings should always be indicated in a table note.